This is how many CS conferences already work (even with public anonymous peer review, go to openreview.net to see it in action). It does seem to be better, although the frustration level for researchers is not really less.

Edit: also, in CS there is a norm that reviewers will not go out of their way to figure out if a submitted paper has been previously posted on arXiv. I don't think it's possible to have perfect anonymity without forbidding researchers from publicly talking about work in progress, so this seems like a reasonable compromise.